In the halftone printing art variations in the density of a color are represented by variations in the size (area) of small dots on a grid pattern. This permits the visual detection of shades of gray and color tone. A patent of interest for its teaching of dot size being a function of density is U.S. Pat. No. 4,680,645, entitled "Method For Rendering Gray Scale Images With Variable Dot Sizes" by Dispoto et al. With such methods the dots themselves do not have to be circular in shape but can have any number of shapes. With the advent of digital computers and digital printers into the printing art, digital bits, representing the desired sizing and shape of the dots, are stored and accessed from the computer or printer's memory and are used to cause the desired printing of the images onto hard copy. In digital systems the halftone dot shapes may be stored either as arrays of threshold values(e.g. 64.times.64.times.8 bits) or as arrays of bitmaps (e.g. 64.times.64.times.256 bits). The quality of the shape of the dots is a function of the number of bits (sample points) that are used in the printing process. Obviously, as more bits are used to increase the quality of the formed dot the greater will be the use of the computer or printer's memory space. In addition, with more bits stored in memory the longer it will take, in terms of access time, to call forth all the bits needed to drive the printing device. In the art, the number of sample points used to represent an image in an array of spaced rows and columns of sample points is called the mesh. It has been shown that there is an improvement in the quality of formed dots when the number of sample points in an array increases. What is known is that sampling in a 256.times.256 array or a 128.times.128 array, in place of a 64.times.64 array, achieves only a slightly improved dot shape at the cost of 16 times and 4 times, respectively, in the amount of memory required to store the threshold or bitmap values.
In addition to the above mentioned increase in memory requirement, to achieve an increase in the quality of the formed dots when a digital screening pattern is used to print out the dots a problem of automoire or patterning is created. This is caused by the step of re-sampling the already sampled dot shapes. These problems have caused a great deal of development time to be spent looking for the "magic" combinations of screen rulings and screen angles which will produce dots without moire through the entire range of dot sizes. The present invention provides an improved solution to these problems.